Solve the Matrix Equation [[4,-21],[13,6],[8,-9]]+x=[[7,-16],[12,19],[1,0]]

$[\begin{array}{c} 4 & - 21 \\ 13 & 6 \\ 8 & - 9 \end{array}] + x = [\begin{array}{c} 7 & - 16 \\ 12 & 19 \\ 1 & 0 \end{array}]$

Step 1

Subtract the matrix from both sides of the equation.

$[\begin{array}{c} 4 & - 21 \\ 13 & 6 \\ 8 & - 9 \end{array}] + X - [\begin{array}{c} 4 & - 21 \\ 13 & 6 \\ 8 & - 9 \end{array}] = [\begin{array}{c} 7 & - 16 \\ 12 & 19 \\ 1 & 0 \end{array}] - [\begin{array}{c} 4 & - 21 \\ 13 & 6 \\ 8 & - 9 \end{array}]$

Step 2

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 4 - 4 & - 21 - (- 21) \\ 13 - 13 & 6 - 6 \\ 8 - 8 & - 9 - (- 9) \end{array}] + X = [\begin{array}{c} 7 & - 16 \\ 12 & 19 \\ 1 & 0 \end{array}] - [\begin{array}{c} 4 & - 21 \\ 13 & 6 \\ 8 & - 9 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 4 - 4 & - 21 - (- 21) \\ 13 - 13 & 6 - 6 \\ 8 - 8 & - 9 - (- 9) \end{array}]$ .

Simplify $4 - 4$ .

$[\begin{array}{c} 0 & - 21 - (- 21) \\ 13 - 13 & 6 - 6 \\ 8 - 8 & - 9 - (- 9) \end{array}] + X = [\begin{array}{c} 7 & - 16 \\ 12 & 19 \\ 1 & 0 \end{array}] - [\begin{array}{c} 4 & - 21 \\ 13 & 6 \\ 8 & - 9 \end{array}]$

Simplify $- 21 - (- 21)$ .

$[\begin{array}{c} 0 & 0 \\ 13 - 13 & 6 - 6 \\ 8 - 8 & - 9 - (- 9) \end{array}] + X = [\begin{array}{c} 7 & - 16 \\ 12 & 19 \\ 1 & 0 \end{array}] - [\begin{array}{c} 4 & - 21 \\ 13 & 6 \\ 8 & - 9 \end{array}]$

Simplify $13 - 13$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 6 - 6 \\ 8 - 8 & - 9 - (- 9) \end{array}] + X = [\begin{array}{c} 7 & - 16 \\ 12 & 19 \\ 1 & 0 \end{array}] - [\begin{array}{c} 4 & - 21 \\ 13 & 6 \\ 8 & - 9 \end{array}]$

Simplify $6 - 6$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 8 - 8 & - 9 - (- 9) \end{array}] + X = [\begin{array}{c} 7 & - 16 \\ 12 & 19 \\ 1 & 0 \end{array}] - [\begin{array}{c} 4 & - 21 \\ 13 & 6 \\ 8 & - 9 \end{array}]$

Simplify $8 - 8$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & - 9 - (- 9) \end{array}] + X = [\begin{array}{c} 7 & - 16 \\ 12 & 19 \\ 1 & 0 \end{array}] - [\begin{array}{c} 4 & - 21 \\ 13 & 6 \\ 8 & - 9 \end{array}]$

Simplify $- 9 - (- 9)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 7 & - 16 \\ 12 & 19 \\ 1 & 0 \end{array}] - [\begin{array}{c} 4 & - 21 \\ 13 & 6 \\ 8 & - 9 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 7 - 4 & - 16 - (- 21) \\ 12 - 13 & 19 - 6 \\ 1 - 8 & 0 - (- 9) \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 7 - 4 & - 16 - (- 21) \\ 12 - 13 & 19 - 6 \\ 1 - 8 & 0 - (- 9) \end{array}]$ .

Simplify $7 - 4$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 3 & - 16 - (- 21) \\ 12 - 13 & 19 - 6 \\ 1 - 8 & 0 - (- 9) \end{array}]$

Simplify $- 16 - (- 21)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 3 & 5 \\ 12 - 13 & 19 - 6 \\ 1 - 8 & 0 - (- 9) \end{array}]$

Simplify $12 - 13$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 3 & 5 \\ - 1 & 19 - 6 \\ 1 - 8 & 0 - (- 9) \end{array}]$

Simplify $19 - 6$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 3 & 5 \\ - 1 & 13 \\ 1 - 8 & 0 - (- 9) \end{array}]$

Simplify $1 - 8$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 3 & 5 \\ - 1 & 13 \\ - 7 & 0 - (- 9) \end{array}]$

Simplify $0 - (- 9)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 3 & 5 \\ - 1 & 13 \\ - 7 & 9 \end{array}]$

Adding the null matrix to any matrix is a matrix itself.

$X = [\begin{array}{c} 3 & 5 \\ - 1 & 13 \\ - 7 & 9 \end{array}]$

Step 3

The matrix is in the most simplified form.

$X = [\begin{array}{c} 3 & 5 \\ - 1 & 13 \\ - 7 & 9 \end{array}]$

Solve the Matrix Equation [[4,-21],[13,6],[8,-9]]+x=[[7,-16],[12,19],[1,0]]

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